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Diffstat (limited to 'libFDK/src/fixpoint_math.cpp')
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diff --git a/libFDK/src/fixpoint_math.cpp b/libFDK/src/fixpoint_math.cpp new file mode 100644 index 0000000..000820c --- /dev/null +++ b/libFDK/src/fixpoint_math.cpp @@ -0,0 +1,853 @@ + +/* ----------------------------------------------------------------------------------------------------------- +Software License for The Fraunhofer FDK AAC Codec Library for Android + +© Copyright 1995 - 2012 Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V. + All rights reserved. + + 1. INTRODUCTION +The Fraunhofer FDK AAC Codec Library for Android ("FDK AAC Codec") is software that implements +the MPEG Advanced Audio Coding ("AAC") encoding and decoding scheme for digital audio. +This FDK AAC Codec software is intended to be used on a wide variety of Android devices. + +AAC's HE-AAC and HE-AAC v2 versions are regarded as today's most efficient general perceptual +audio codecs. AAC-ELD is considered the best-performing full-bandwidth communications codec by +independent studies and is widely deployed. AAC has been standardized by ISO and IEC as part +of the MPEG specifications. + +Patent licenses for necessary patent claims for the FDK AAC Codec (including those of Fraunhofer) +may be obtained through Via Licensing (www.vialicensing.com) or through the respective patent owners +individually for the purpose of encoding or decoding bit streams in products that are compliant with +the ISO/IEC MPEG audio standards. Please note that most manufacturers of Android devices already license +these patent claims through Via Licensing or directly from the patent owners, and therefore FDK AAC Codec +software may already be covered under those patent licenses when it is used for those licensed purposes only. + +Commercially-licensed AAC software libraries, including floating-point versions with enhanced sound quality, +are also available from Fraunhofer. Users are encouraged to check the Fraunhofer website for additional +applications information and documentation. + +2. COPYRIGHT LICENSE + +Redistribution and use in source and binary forms, with or without modification, are permitted without +payment of copyright license fees provided that you satisfy the following conditions: + +You must retain the complete text of this software license in redistributions of the FDK AAC Codec or +your modifications thereto in source code form. + +You must retain the complete text of this software license in the documentation and/or other materials +provided with redistributions of the FDK AAC Codec or your modifications thereto in binary form. +You must make available free of charge copies of the complete source code of the FDK AAC Codec and your +modifications thereto to recipients of copies in binary form. + +The name of Fraunhofer may not be used to endorse or promote products derived from this library without +prior written permission. + +You may not charge copyright license fees for anyone to use, copy or distribute the FDK AAC Codec +software or your modifications thereto. + +Your modified versions of the FDK AAC Codec must carry prominent notices stating that you changed the software +and the date of any change. For modified versions of the FDK AAC Codec, the term +"Fraunhofer FDK AAC Codec Library for Android" must be replaced by the term +"Third-Party Modified Version of the Fraunhofer FDK AAC Codec Library for Android." + +3. NO PATENT LICENSE + +NO EXPRESS OR IMPLIED LICENSES TO ANY PATENT CLAIMS, including without limitation the patents of Fraunhofer, +ARE GRANTED BY THIS SOFTWARE LICENSE. Fraunhofer provides no warranty of patent non-infringement with +respect to this software. + +You may use this FDK AAC Codec software or modifications thereto only for purposes that are authorized +by appropriate patent licenses. + +4. DISCLAIMER + +This FDK AAC Codec software is provided by Fraunhofer on behalf of the copyright holders and contributors +"AS IS" and WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES, including but not limited to the implied warranties +of merchantability and fitness for a particular purpose. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR +CONTRIBUTORS BE LIABLE for any direct, indirect, incidental, special, exemplary, or consequential damages, +including but not limited to procurement of substitute goods or services; loss of use, data, or profits, +or business interruption, however caused and on any theory of liability, whether in contract, strict +liability, or tort (including negligence), arising in any way out of the use of this software, even if +advised of the possibility of such damage. + +5. CONTACT INFORMATION + +Fraunhofer Institute for Integrated Circuits IIS +Attention: Audio and Multimedia Departments - FDK AAC LL +Am Wolfsmantel 33 +91058 Erlangen, Germany + +www.iis.fraunhofer.de/amm +amm-info@iis.fraunhofer.de +----------------------------------------------------------------------------------------------------------- */ + +/*************************** Fraunhofer IIS FDK Tools ********************** + + Author(s): M. Gayer + Description: Fixed point specific mathematical functions + +******************************************************************************/ + +#include "fixpoint_math.h" + + +#define MAX_LD_PRECISION 10 +#define LD_PRECISION 10 + +/* Taylor series coeffcients for ln(1-x), centered at 0 (MacLaurin polinomial). */ +#ifndef LDCOEFF_16BIT +LNK_SECTION_CONSTDATA_L1 +static const FIXP_DBL ldCoeff[MAX_LD_PRECISION] = { + FL2FXCONST_DBL(-1.0), + FL2FXCONST_DBL(-1.0/2.0), + FL2FXCONST_DBL(-1.0/3.0), + FL2FXCONST_DBL(-1.0/4.0), + FL2FXCONST_DBL(-1.0/5.0), + FL2FXCONST_DBL(-1.0/6.0), + FL2FXCONST_DBL(-1.0/7.0), + FL2FXCONST_DBL(-1.0/8.0), + FL2FXCONST_DBL(-1.0/9.0), + FL2FXCONST_DBL(-1.0/10.0) +}; +#else +LNK_SECTION_CONSTDATA_L1 +static const FIXP_SGL ldCoeff[MAX_LD_PRECISION] = { + FL2FXCONST_SGL(-1.0), + FL2FXCONST_SGL(-1.0/2.0), + FL2FXCONST_SGL(-1.0/3.0), + FL2FXCONST_SGL(-1.0/4.0), + FL2FXCONST_SGL(-1.0/5.0), + FL2FXCONST_SGL(-1.0/6.0), + FL2FXCONST_SGL(-1.0/7.0), + FL2FXCONST_SGL(-1.0/8.0), + FL2FXCONST_SGL(-1.0/9.0), + FL2FXCONST_SGL(-1.0/10.0) +}; +#endif + +/***************************************************************************** + + functionname: CalcLdData + description: Delivers the Logarithm Dualis ld(op)/LD_DATA_SCALING with polynomial approximation. + input: Input op is assumed to be double precision fractional 0 < op < 1.0 + This function does not accept negative values. + output: For op == 0, the result is saturated to -1.0 + This function does not return positive values since input values are treated as fractional values. + It does not make sense to input an integer value into this function (and expect a positive output value) + since input values are treated as fractional values. + +*****************************************************************************/ + +LNK_SECTION_CODE_L1 +FIXP_DBL CalcLdData(FIXP_DBL op) +{ + return fLog2(op, 0); +} + + +/***************************************************************************** + functionname: LdDataVector +*****************************************************************************/ +LNK_SECTION_CODE_L1 +void LdDataVector( FIXP_DBL *srcVector, + FIXP_DBL *destVector, + INT n) +{ + INT i; + for ( i=0; i<n; i++) { + destVector[i] = CalcLdData(srcVector[i]); + } +} + + + +#define MAX_POW2_PRECISION 8 +#ifndef SINETABLE_16BIT + #define POW2_PRECISION MAX_POW2_PRECISION +#else + #define POW2_PRECISION 5 +#endif + +/* + Taylor series coefficients of the function x^2. The first coefficient is + ommited (equal to 1.0). + + pow2Coeff[i-1] = (1/i!) d^i(2^x)/dx^i, i=1..MAX_POW2_PRECISION + To evaluate the taylor series around x = 0, the coefficients are: 1/!i * ln(2)^i + */ +#ifndef POW2COEFF_16BIT +LNK_SECTION_CONSTDATA_L1 +static const FIXP_DBL pow2Coeff[MAX_POW2_PRECISION] = { + FL2FXCONST_DBL(0.693147180559945309417232121458177), /* ln(2)^1 /1! */ + FL2FXCONST_DBL(0.240226506959100712333551263163332), /* ln(2)^2 /2! */ + FL2FXCONST_DBL(0.0555041086648215799531422637686218), /* ln(2)^3 /3! */ + FL2FXCONST_DBL(0.00961812910762847716197907157365887), /* ln(2)^4 /4! */ + FL2FXCONST_DBL(0.00133335581464284434234122219879962), /* ln(2)^5 /5! */ + FL2FXCONST_DBL(1.54035303933816099544370973327423e-4), /* ln(2)^6 /6! */ + FL2FXCONST_DBL(1.52527338040598402800254390120096e-5), /* ln(2)^7 /7! */ + FL2FXCONST_DBL(1.32154867901443094884037582282884e-6) /* ln(2)^8 /8! */ +}; +#else +LNK_SECTION_CONSTDATA_L1 +static const FIXP_SGL pow2Coeff[MAX_POW2_PRECISION] = { + FL2FXCONST_SGL(0.693147180559945309417232121458177), /* ln(2)^1 /1! */ + FL2FXCONST_SGL(0.240226506959100712333551263163332), /* ln(2)^2 /2! */ + FL2FXCONST_SGL(0.0555041086648215799531422637686218), /* ln(2)^3 /3! */ + FL2FXCONST_SGL(0.00961812910762847716197907157365887), /* ln(2)^4 /4! */ + FL2FXCONST_SGL(0.00133335581464284434234122219879962), /* ln(2)^5 /5! */ + FL2FXCONST_SGL(1.54035303933816099544370973327423e-4), /* ln(2)^6 /6! */ + FL2FXCONST_SGL(1.52527338040598402800254390120096e-5), /* ln(2)^7 /7! */ + FL2FXCONST_SGL(1.32154867901443094884037582282884e-6) /* ln(2)^8 /8! */ +}; +#endif + + + +/***************************************************************************** + + functionname: mul_dbl_sgl_rnd + description: Multiply with round. +*****************************************************************************/ + +/* for rounding a dfract to fract */ +#define ACCU_R (LONG) 0x00008000 + +LNK_SECTION_CODE_L1 +FIXP_DBL mul_dbl_sgl_rnd (const FIXP_DBL op1, const FIXP_SGL op2) +{ + FIXP_DBL prod; + LONG v = (LONG)(op1); + SHORT u = (SHORT)(op2); + + LONG low = u*(v&SGL_MASK); + low = (low+(ACCU_R>>1)) >> (FRACT_BITS-1); /* round */ + LONG high = u * ((v>>FRACT_BITS)<<1); + + prod = (LONG)(high+low); + + return((FIXP_DBL)prod); +} + + +/***************************************************************************** + + functionname: CalcInvLdData + description: Delivers the inverse of function CalcLdData(). + Delivers 2^(op*LD_DATA_SCALING) + input: Input op is assumed to be fractional -1.0 < op < 1.0 + output: For op == 0, the result is MAXVAL_DBL (almost 1.0). + For negative input values the output should be treated as a positive fractional value. + For positive input values the output should be treated as a positive integer value. + This function does not output negative values. + +*****************************************************************************/ +LNK_SECTION_CODE_L1 +FIXP_DBL CalcInvLdData(FIXP_DBL op) +{ + FIXP_DBL result_m; + + if ( op == FL2FXCONST_DBL(0.0f) ) { + result_m = (FIXP_DBL)MAXVAL_DBL; + } + else if ( op < FL2FXCONST_DBL(0.0f) ) { + result_m = f2Pow(op, LD_DATA_SHIFT); + } + else { + int result_e; + + result_m = f2Pow(op, LD_DATA_SHIFT, &result_e); + result_e = fixMin(fixMax(result_e+1-(DFRACT_BITS-1), -(DFRACT_BITS-1)), (DFRACT_BITS-1)); /* rounding and saturation */ + + if ( (result_e>0) && ( result_m > (((FIXP_DBL)MAXVAL_DBL)>>result_e) ) ) { + result_m = (FIXP_DBL)MAXVAL_DBL; /* saturate to max representable value */ + } + else { + result_m = (scaleValue(result_m, result_e)+(FIXP_DBL)1)>>1; /* descale result + rounding */ + } + } + return result_m; +} + + + + + +/***************************************************************************** + functionname: InitLdInt and CalcLdInt + description: Create and access table with integer LdData (0 to 193) +*****************************************************************************/ + + + LNK_SECTION_CONSTDATA_L1 + static const FIXP_DBL ldIntCoeff[] = { + 0x80000001, 0x00000000, 0x02000000, 0x032b8034, 0x04000000, 0x04a4d3c2, 0x052b8034, 0x059d5da0, + 0x06000000, 0x06570069, 0x06a4d3c2, 0x06eb3a9f, 0x072b8034, 0x0766a009, 0x079d5da0, 0x07d053f7, + 0x08000000, 0x082cc7ee, 0x08570069, 0x087ef05b, 0x08a4d3c2, 0x08c8ddd4, 0x08eb3a9f, 0x090c1050, + 0x092b8034, 0x0949a785, 0x0966a009, 0x0982809d, 0x099d5da0, 0x09b74949, 0x09d053f7, 0x09e88c6b, + 0x0a000000, 0x0a16bad3, 0x0a2cc7ee, 0x0a423162, 0x0a570069, 0x0a6b3d79, 0x0a7ef05b, 0x0a92203d, + 0x0aa4d3c2, 0x0ab7110e, 0x0ac8ddd4, 0x0ada3f60, 0x0aeb3a9f, 0x0afbd42b, 0x0b0c1050, 0x0b1bf312, + 0x0b2b8034, 0x0b3abb40, 0x0b49a785, 0x0b584822, 0x0b66a009, 0x0b74b1fd, 0x0b82809d, 0x0b900e61, + 0x0b9d5da0, 0x0baa708f, 0x0bb74949, 0x0bc3e9ca, 0x0bd053f7, 0x0bdc899b, 0x0be88c6b, 0x0bf45e09, + 0x0c000000, 0x0c0b73cb, 0x0c16bad3, 0x0c21d671, 0x0c2cc7ee, 0x0c379085, 0x0c423162, 0x0c4caba8, + 0x0c570069, 0x0c6130af, 0x0c6b3d79, 0x0c7527b9, 0x0c7ef05b, 0x0c88983f, 0x0c92203d, 0x0c9b8926, + 0x0ca4d3c2, 0x0cae00d2, 0x0cb7110e, 0x0cc0052b, 0x0cc8ddd4, 0x0cd19bb0, 0x0cda3f60, 0x0ce2c97d, + 0x0ceb3a9f, 0x0cf39355, 0x0cfbd42b, 0x0d03fda9, 0x0d0c1050, 0x0d140ca0, 0x0d1bf312, 0x0d23c41d, + 0x0d2b8034, 0x0d3327c7, 0x0d3abb40, 0x0d423b08, 0x0d49a785, 0x0d510118, 0x0d584822, 0x0d5f7cff, + 0x0d66a009, 0x0d6db197, 0x0d74b1fd, 0x0d7ba190, 0x0d82809d, 0x0d894f75, 0x0d900e61, 0x0d96bdad, + 0x0d9d5da0, 0x0da3ee7f, 0x0daa708f, 0x0db0e412, 0x0db74949, 0x0dbda072, 0x0dc3e9ca, 0x0dca258e, + 0x0dd053f7, 0x0dd6753e, 0x0ddc899b, 0x0de29143, 0x0de88c6b, 0x0dee7b47, 0x0df45e09, 0x0dfa34e1, + 0x0e000000, 0x0e05bf94, 0x0e0b73cb, 0x0e111cd2, 0x0e16bad3, 0x0e1c4dfb, 0x0e21d671, 0x0e275460, + 0x0e2cc7ee, 0x0e323143, 0x0e379085, 0x0e3ce5d8, 0x0e423162, 0x0e477346, 0x0e4caba8, 0x0e51daa8, + 0x0e570069, 0x0e5c1d0b, 0x0e6130af, 0x0e663b74, 0x0e6b3d79, 0x0e7036db, 0x0e7527b9, 0x0e7a1030, + 0x0e7ef05b, 0x0e83c857, 0x0e88983f, 0x0e8d602e, 0x0e92203d, 0x0e96d888, 0x0e9b8926, 0x0ea03232, + 0x0ea4d3c2, 0x0ea96df0, 0x0eae00d2, 0x0eb28c7f, 0x0eb7110e, 0x0ebb8e96, 0x0ec0052b, 0x0ec474e4, + 0x0ec8ddd4, 0x0ecd4012, 0x0ed19bb0, 0x0ed5f0c4, 0x0eda3f60, 0x0ede8797, 0x0ee2c97d, 0x0ee70525, + 0x0eeb3a9f, 0x0eef69ff, 0x0ef39355, 0x0ef7b6b4, 0x0efbd42b, 0x0effebcd, 0x0f03fda9, 0x0f0809cf, + 0x0f0c1050, 0x0f10113b, 0x0f140ca0, 0x0f18028d, 0x0f1bf312, 0x0f1fde3d, 0x0f23c41d, 0x0f27a4c0, + 0x0f2b8034 + }; + + + LNK_SECTION_INITCODE + void InitLdInt() + { + /* nothing to do! Use preinitialized logarithm table */ + } + + + +LNK_SECTION_CODE_L1 +FIXP_DBL CalcLdInt(INT i) +{ + /* calculates ld(op)/LD_DATA_SCALING */ + /* op is assumed to be an integer value between 1 and 193 */ + + FDK_ASSERT((193>0) && ((FIXP_DBL)ldIntCoeff[0]==(FIXP_DBL)0x80000001)); /* tab has to be initialized */ + + if ((i>0)&&(i<193)) + return ldIntCoeff[i]; + else + { + return (0); + } +} + + +/***************************************************************************** + + functionname: invSqrtNorm2 + description: delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT + +*****************************************************************************/ +#define SQRT_BITS 7 +#define SQRT_VALUES 128 +#define SQRT_BITS_MASK 0x7f + +LNK_SECTION_CONSTDATA_L1 +static const FIXP_DBL invSqrtTab[SQRT_VALUES] = { + 0x5a827999, 0x5a287e03, 0x59cf8cbb, 0x5977a0ab, 0x5920b4de, 0x58cac480, 0x5875cade, 0x5821c364, + 0x57cea99c, 0x577c792f, 0x572b2ddf, 0x56dac38d, 0x568b3631, 0x563c81df, 0x55eea2c3, 0x55a19521, + 0x55555555, 0x5509dfd0, 0x54bf311a, 0x547545d0, 0x542c1aa3, 0x53e3ac5a, 0x539bf7cc, 0x5354f9e6, + 0x530eafa4, 0x52c91617, 0x52842a5e, 0x523fe9ab, 0x51fc513f, 0x51b95e6b, 0x51770e8e, 0x51355f19, + 0x50f44d88, 0x50b3d768, 0x5073fa4f, 0x5034b3e6, 0x4ff601df, 0x4fb7e1f9, 0x4f7a5201, 0x4f3d4fce, + 0x4f00d943, 0x4ec4ec4e, 0x4e8986e9, 0x4e4ea718, 0x4e144ae8, 0x4dda7072, 0x4da115d9, 0x4d683948, + 0x4d2fd8f4, 0x4cf7f31b, 0x4cc08604, 0x4c898fff, 0x4c530f64, 0x4c1d0293, 0x4be767f5, 0x4bb23df9, + 0x4b7d8317, 0x4b4935ce, 0x4b1554a6, 0x4ae1de2a, 0x4aaed0f0, 0x4a7c2b92, 0x4a49ecb3, 0x4a1812fa, + 0x49e69d16, 0x49b589bb, 0x4984d7a4, 0x49548591, 0x49249249, 0x48f4fc96, 0x48c5c34a, 0x4896e53c, + 0x48686147, 0x483a364c, 0x480c6331, 0x47dee6e0, 0x47b1c049, 0x4784ee5f, 0x4758701c, 0x472c447c, + 0x47006a80, 0x46d4e130, 0x46a9a793, 0x467ebcb9, 0x46541fb3, 0x4629cf98, 0x45ffcb80, 0x45d61289, + 0x45aca3d5, 0x45837e88, 0x455aa1ca, 0x45320cc8, 0x4509beb0, 0x44e1b6b4, 0x44b9f40b, 0x449275ec, + 0x446b3b95, 0x44444444, 0x441d8f3b, 0x43f71bbe, 0x43d0e917, 0x43aaf68e, 0x43854373, 0x435fcf14, + 0x433a98c5, 0x43159fdb, 0x42f0e3ae, 0x42cc6397, 0x42a81ef5, 0x42841527, 0x4260458d, 0x423caf8c, + 0x4219528b, 0x41f62df1, 0x41d3412a, 0x41b08ba1, 0x418e0cc7, 0x416bc40d, 0x4149b0e4, 0x4127d2c3, + 0x41062920, 0x40e4b374, 0x40c3713a, 0x40a261ef, 0x40818511, 0x4060da21, 0x404060a1, 0x40201814 +}; + +LNK_SECTION_INITCODE +void InitInvSqrtTab() +{ + /* nothing to do ! + use preinitialized square root table + */ +} + + + +#if !defined(FUNCTION_invSqrtNorm2) +/***************************************************************************** + delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT, + i.e. the denormalized result is 1/sqrt(op) = invSqrtNorm(op) * 2^(shift) + uses Newton-iteration for approximation + Q(n+1) = Q(n) + Q(n) * (0.5 - 2 * V * Q(n)^2) + with Q = 0.5* V ^-0.5; 0.5 <= V < 1.0 +*****************************************************************************/ +FIXP_DBL invSqrtNorm2(FIXP_DBL op, INT *shift) +{ + + FIXP_DBL val = op ; + FIXP_DBL reg1, reg2, regtmp ; + + if (val == FL2FXCONST_DBL(0.0)) { + *shift = 1 ; + return((LONG)1); /* minimum positive value */ + } + + + /* normalize input, calculate shift value */ + FDK_ASSERT(val > FL2FXCONST_DBL(0.0)); + *shift = fNormz(val) - 1; /* CountLeadingBits() is not necessary here since test value is always > 0 */ + val <<=*shift ; /* normalized input V */ + *shift+=2 ; /* bias for exponent */ + + /* Newton iteration of 1/sqrt(V) */ + reg1 = invSqrtTab[ (INT)(val>>(DFRACT_BITS-1-(SQRT_BITS+1))) & SQRT_BITS_MASK ]; + reg2 = FL2FXCONST_DBL(0.0625f); /* 0.5 >> 3 */ + + regtmp= fPow2Div2(reg1); /* a = Q^2 */ + regtmp= reg2 - fMultDiv2(regtmp, val); /* b = 0.5 - 2 * V * Q^2 */ + reg1 += (fMultDiv2(regtmp, reg1)<<4); /* Q = Q + Q*b */ + + /* calculate the output exponent = input exp/2 */ + if (*shift & 0x00000001) { /* odd shift values ? */ + reg2 = FL2FXCONST_DBL(0.707106781186547524400844362104849f); /* 1/sqrt(2); */ + reg1 = fMultDiv2(reg1, reg2) << 2; + } + + *shift = *shift>>1; + + return(reg1); +} +#endif /* !defined(FUNCTION_invSqrtNorm2) */ + +/***************************************************************************** + + functionname: sqrtFixp + description: delivers sqrt(op) + +*****************************************************************************/ +FIXP_DBL sqrtFixp(FIXP_DBL op) +{ + INT tmp_exp = 0; + FIXP_DBL tmp_inv = invSqrtNorm2(op, &tmp_exp); + + FDK_ASSERT(tmp_exp > 0) ; + return( (FIXP_DBL) ( fMultDiv2( (op<<(tmp_exp-1)), tmp_inv ) << 2 )); +} + + +#if !defined(FUNCTION_schur_div) +/***************************************************************************** + + functionname: schur_div + description: delivers op1/op2 with op3-bit accuracy + +*****************************************************************************/ + + +FIXP_DBL schur_div(FIXP_DBL num, FIXP_DBL denum, INT count) +{ + INT L_num = (LONG)num>>1; + INT L_denum = (LONG)denum>>1; + INT div = 0; + INT k = count; + + FDK_ASSERT (num>=(FIXP_DBL)0); + FDK_ASSERT (denum>(FIXP_DBL)0); + FDK_ASSERT (num <= denum); + + if (L_num != 0) + while (--k) + { + div <<= 1; + L_num <<= 1; + if (L_num >= L_denum) + { + L_num -= L_denum; + div++; + } + } + return (FIXP_DBL)(div << (DFRACT_BITS - count)); +} + + +#endif /* !defined(FUNCTION_schur_div) */ + + +#ifndef FUNCTION_fMultNorm +FIXP_DBL fMultNorm(FIXP_DBL f1, FIXP_DBL f2, INT *result_e) +{ + INT product = 0; + INT norm_f1, norm_f2; + + if ( (f1 == (FIXP_DBL)0) || (f2 == (FIXP_DBL)0) ) { + *result_e = 0; + return (FIXP_DBL)0; + } + norm_f1 = CountLeadingBits(f1); + f1 = f1 << norm_f1; + norm_f2 = CountLeadingBits(f2); + f2 = f2 << norm_f2; + + product = fMult(f1, f2); + *result_e = - (norm_f1 + norm_f2); + + return (FIXP_DBL)product; +} +#endif + +#ifndef FUNCTION_fDivNorm +FIXP_DBL fDivNorm(FIXP_DBL L_num, FIXP_DBL L_denum, INT *result_e) +{ + FIXP_DBL div; + INT norm_num, norm_den; + + FDK_ASSERT (L_num >= (FIXP_DBL)0); + FDK_ASSERT (L_denum > (FIXP_DBL)0); + + if(L_num == (FIXP_DBL)0) + { + *result_e = 0; + return ((FIXP_DBL)0); + } + + norm_num = CountLeadingBits(L_num); + L_num = L_num << norm_num; + L_num = L_num >> 1; + *result_e = - norm_num + 1; + + norm_den = CountLeadingBits(L_denum); + L_denum = L_denum << norm_den; + *result_e -= - norm_den; + + div = schur_div(L_num, L_denum, FRACT_BITS); + + return div; +} +#endif /* !FUNCTION_fDivNorm */ + +#ifndef FUNCTION_fDivNorm +FIXP_DBL fDivNorm(FIXP_DBL num, FIXP_DBL denom) +{ + INT e; + FIXP_DBL res; + + FDK_ASSERT (denom >= num); + + res = fDivNorm(num, denom, &e); + + /* Avoid overflow since we must output a value with exponent 0 + there is no other choice than saturating to almost 1.0f */ + if(res == (FIXP_DBL)(1<<(DFRACT_BITS-2)) && e == 1) + { + res = (FIXP_DBL)MAXVAL_DBL; + } + else + { + res = scaleValue(res, e); + } + + return res; +} +#endif /* !FUNCTION_fDivNorm */ + +#ifndef FUNCTION_fDivNormHighPrec +FIXP_DBL fDivNormHighPrec(FIXP_DBL num, FIXP_DBL denom, INT *result_e) +{ + FIXP_DBL div; + INT norm_num, norm_den; + + FDK_ASSERT (num >= (FIXP_DBL)0); + FDK_ASSERT (denom > (FIXP_DBL)0); + + if(num == (FIXP_DBL)0) + { + *result_e = 0; + return ((FIXP_DBL)0); + } + + norm_num = CountLeadingBits(num); + num = num << norm_num; + num = num >> 1; + *result_e = - norm_num + 1; + + norm_den = CountLeadingBits(denom); + denom = denom << norm_den; + *result_e -= - norm_den; + + div = schur_div(num, denom, 31); + return div; +} +#endif /* !FUNCTION_fDivNormHighPrec */ + + + +FIXP_DBL CalcLog2(FIXP_DBL base_m, INT base_e, INT *result_e) +{ + return fLog2(base_m, base_e, result_e); +} + +FIXP_DBL f2Pow( + const FIXP_DBL exp_m, const INT exp_e, + INT *result_e + ) +{ + FIXP_DBL frac_part, result_m; + INT int_part; + + if (exp_e > 0) + { + INT exp_bits = DFRACT_BITS-1 - exp_e; + int_part = exp_m >> exp_bits; + frac_part = exp_m - (FIXP_DBL)(int_part << exp_bits); + frac_part = frac_part << exp_e; + } + else + { + int_part = 0; + frac_part = exp_m >> -exp_e; + } + + /* Best accuracy is around 0, so try to get there with the fractional part. */ + if( frac_part > FL2FXCONST_DBL(0.5f) ) + { + int_part = int_part + 1; + frac_part = frac_part + FL2FXCONST_DBL(-1.0f); + } + if( frac_part < FL2FXCONST_DBL(-0.5f) ) + { + int_part = int_part - 1; + frac_part = -(FL2FXCONST_DBL(-1.0f) - frac_part); + } + + /* Evaluate taylor polynomial which approximates 2^x */ + { + FIXP_DBL p; + + /* result_m ~= 2^frac_part */ + p = frac_part; + /* First taylor series coefficient a_0 = 1.0, scaled by 0.5 due to fMultDiv2(). */ + result_m = FL2FXCONST_DBL(1.0f/2.0f); + for (INT i = 0; i < POW2_PRECISION; i++) { + /* next taylor series term: a_i * x^i, x=0 */ + result_m = fMultAddDiv2(result_m, pow2Coeff[i], p); + p = fMult(p, frac_part); + } + } + + /* "+ 1" compensates fMultAddDiv2() of the polynomial evaluation above. */ + *result_e = int_part + 1; + + return result_m; +} + +FIXP_DBL f2Pow( + const FIXP_DBL exp_m, const INT exp_e + ) +{ + FIXP_DBL result_m; + INT result_e; + + result_m = f2Pow(exp_m, exp_e, &result_e); + result_e = fixMin(DFRACT_BITS-1,fixMax(-(DFRACT_BITS-1),result_e)); + + return scaleValue(result_m, result_e); +} + +FIXP_DBL fPow( + FIXP_DBL base_m, INT base_e, + FIXP_DBL exp_m, INT exp_e, + INT *result_e + ) +{ + INT ans_lg2_e, baselg2_e; + FIXP_DBL base_lg2, ans_lg2, result; + + /* Calc log2 of base */ + base_lg2 = fLog2(base_m, base_e, &baselg2_e); + + /* Prepare exp */ + { + INT leadingBits; + + leadingBits = CountLeadingBits(fAbs(exp_m)); + exp_m = exp_m << leadingBits; + exp_e -= leadingBits; + } + + /* Calc base pow exp */ + ans_lg2 = fMult(base_lg2, exp_m); + ans_lg2_e = exp_e + baselg2_e; + + /* Calc antilog */ + result = f2Pow(ans_lg2, ans_lg2_e, result_e); + + return result; +} + +FIXP_DBL fLdPow( + FIXP_DBL baseLd_m, + INT baseLd_e, + FIXP_DBL exp_m, INT exp_e, + INT *result_e + ) +{ + INT ans_lg2_e; + FIXP_DBL ans_lg2, result; + + /* Prepare exp */ + { + INT leadingBits; + + leadingBits = CountLeadingBits(fAbs(exp_m)); + exp_m = exp_m << leadingBits; + exp_e -= leadingBits; + } + + /* Calc base pow exp */ + ans_lg2 = fMult(baseLd_m, exp_m); + ans_lg2_e = exp_e + baseLd_e; + + /* Calc antilog */ + result = f2Pow(ans_lg2, ans_lg2_e, result_e); + + return result; +} + +FIXP_DBL fLdPow( + FIXP_DBL baseLd_m, INT baseLd_e, + FIXP_DBL exp_m, INT exp_e + ) +{ + FIXP_DBL result_m; + int result_e; + + result_m = fLdPow(baseLd_m, baseLd_e, exp_m, exp_e, &result_e); + + return SATURATE_SHIFT(result_m, -result_e, DFRACT_BITS); +} + +FIXP_DBL fPowInt( + FIXP_DBL base_m, INT base_e, + INT exp, + INT *pResult_e + ) +{ + FIXP_DBL result; + + if (exp != 0) { + INT result_e = 0; + + if (base_m != (FIXP_DBL)0) { + { + INT leadingBits; + leadingBits = CountLeadingBits( base_m ); + base_m <<= leadingBits; + base_e -= leadingBits; + } + + result = base_m; + + { + int i; + for (i = 1; i < fAbs(exp); i++) { + result = fMult(result, base_m); + } + } + + if (exp < 0) { + /* 1.0 / ans */ + result = fDivNorm( FL2FXCONST_DBL(0.5f), result, &result_e ); + result_e++; + } else { + int ansScale = CountLeadingBits( result ); + result <<= ansScale; + result_e -= ansScale; + } + + result_e += exp * base_e; + + } else { + result = (FIXP_DBL)0; + } + *pResult_e = result_e; + } + else { + result = FL2FXCONST_DBL(0.5f); + *pResult_e = 1; + } + + return result; +} + +FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e, INT *result_e) +{ + FIXP_DBL result_m; + + /* Short cut for zero and negative numbers. */ + if ( x_m <= FL2FXCONST_DBL(0.0f) ) { + *result_e = DFRACT_BITS-1; + return FL2FXCONST_DBL(-1.0f); + } + + /* Calculate log2() */ + { + FIXP_DBL px2_m, x2_m; + + /* Move input value x_m * 2^x_e toward 1.0, where the taylor approximation + of the function log(1-x) centered at 0 is most accurate. */ + { + INT b_norm; + + b_norm = fNormz(x_m)-1; + x2_m = x_m << b_norm; + x_e = x_e - b_norm; + } + + /* map x from log(x) domain to log(1-x) domain. */ + x2_m = - (x2_m + FL2FXCONST_DBL(-1.0) ); + + /* Taylor polinomial approximation of ln(1-x) */ + result_m = FL2FXCONST_DBL(0.0); + px2_m = x2_m; + for (int i=0; i<LD_PRECISION; i++) { + result_m = fMultAddDiv2(result_m, ldCoeff[i], px2_m); + px2_m = fMult(px2_m, x2_m); + } + /* Multiply result with 1/ln(2) = 1.0 + 0.442695040888 (get log2(x) from ln(x) result). */ + result_m = fMultAddDiv2(result_m, result_m, FL2FXCONST_DBL(2.0*0.4426950408889634073599246810019)); + + /* Add exponent part. log2(x_m * 2^x_e) = log2(x_m) + x_e */ + if (x_e != 0) + { + int enorm; + + enorm = DFRACT_BITS - fNorm((FIXP_DBL)x_e); + /* The -1 in the right shift of result_m compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/ + result_m = (result_m >> (enorm-1)) + ((FIXP_DBL)x_e << (DFRACT_BITS-1-enorm)); + + *result_e = enorm; + } else { + /* 1 compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/ + *result_e = 1; + } + } + + return result_m; +} + +FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e) +{ + if ( x_m <= FL2FXCONST_DBL(0.0f) ) { + x_m = FL2FXCONST_DBL(-1.0f); + } + else { + INT result_e; + x_m = fLog2(x_m, x_e, &result_e); + x_m = scaleValue(x_m, result_e-LD_DATA_SHIFT); + } + return x_m; +} + + + + |